In internal combustion engines, an amount of air supplied to engine cylinders may be manipulated by engine components. For example, in modern diesel engines, variable geometry turbines (VGT) may be used to increase an amount of air supplied to engine cylinders by varying an angle of turbine stator inlet vanes such that the amount of supplied air is changed.
Such modern diesel engines typically balance providing optimum performance and fuel economy while meeting stringent federal regulations on emissions, such as constraints on particulate matter and nitrogen oxides. To meet these requirements, many diesel engines having a VGT also use an exhaust gas recirculation (EGR) valve having a variable controlled position. The EGR valve re-circulates varying amounts of engine exhaust gases back into the engine cylinders to allow for both a more complete combustion and reduced engine emissions.
Such engines operate over a large range of operating conditions, which may include, for example, engine speed, fuel usage, and engine load, among other conditions, and one or more controllers are embedded in an engine control unit (ECU) to control various engine actuators in response to sensors that detect engine performance. The ECU works to optimize engine performance, emissions, and other such outputs via use of, for example, quadratic solvers.
Accordingly, a need exists for alternative quadratic solvers to provide reduced computational time and an increased accuracy and methods of use of such quadratic solvers.